%------------------------------------------------------------------------------ % File : CARINE---0.734 % Problem : LCL089-1 : TPTP v5.0.0. Released v1.0.0. % Transfm : add_equality % Format : carine % Command : carine %s t=%d xo=off uct=32000 % Computer : art01.cs.miami.edu % Model : i686 i686 % CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz % Memory : 2018MB % OS : Linux 2.6.26.8-57.fc8 % CPULimit : 300s % DateTime : Sat Nov 27 23:55:29 EST 2010 % Result : Unsatisfiable 65.10s % Output : Refutation 65.10s % Verified : % SZS Type : None (Parsing solution fails) % Syntax : Number of formulae : 0 % Comments : %------------------------------------------------------------------------------ %----ERROR: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % Command entered: % /home/graph/tptp/Systems/CARINE---0.734/carine /tmp/SystemOnTPTP11465/LCL/LCL089-1+noeq.car t=300 xo=off uct=32000 % CARINE version 0.734 (Dec 2003) % Initializing tables ... done. % Parsing ... done. % Calculating time slices ... done. % Building Lookup Tables ... done. % Looking for a proof at depth = 1 ... % t = 0 secs [nr = 3] [nf = 0] [nu = 0] [ut = 2] % Looking for a proof at depth = 2 ... % t = 0 secs [nr = 146] [nf = 0] [nu = 56] [ut = 46] % Looking for a proof at depth = 3 ... % t = 0 secs [nr = 368] [nf = 6] [nu = 183] [ut = 46] % Looking for a proof at depth = 4 ... % +================================================+ % | | % | Congratulations!!! ........ A proof was found. | % | | % +================================================+ % Base Clauses and Unit Clauses used in proof: % ============================================ % Base Clauses: % ------------- % B0: ~is_a_theorem_1(implies_2(implies_2(a_0(),b_0()),implies_2(implies_2(b_0(),c_0()),implies_2(a_0(),c_0())))) % B1: is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),implies_2(x2,x0))))) % B2: ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) % Unit Clauses: % -------------- % U1: < d0 v9 dv5 f8 c0 t17 td5 b > is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),implies_2(x2,x0))))) % U4: < d2 v10 dv6 f9 c0 t19 td6 > is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(implies_2(x1,x2),implies_2(x3,x2)),implies_2(x2,x4)),implies_2(x5,implies_2(x2,x4))))) % U5: < d2 v9 dv5 f8 c0 t17 td5 > is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x1)),implies_2(x1,x3)),implies_2(x4,implies_2(x1,x3)))) % U6: < d2 v6 dv4 f5 c0 t11 td5 > is_a_theorem_1(implies_2(x0,implies_2(x1,implies_2(implies_2(x1,x2),implies_2(x3,x2))))) % U7: < d2 v5 dv3 f4 c0 t9 td4 > is_a_theorem_1(implies_2(x0,implies_2(implies_2(x0,x1),implies_2(x2,x1)))) % U8: < d2 v12 dv7 f11 c0 t23 td7 > is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),implies_2(x2,x0)))),x5),implies_2(x6,x5))) % U17: < d2 v8 dv5 f7 c0 t15 td6 > is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(x1,x2),x3),implies_2(implies_2(implies_2(x3,x4),x2),x3)))) % U23: < d2 v10 dv6 f9 c0 t19 td7 > is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(implies_2(implies_2(x1,x2),x3),x1),x4),implies_2(implies_2(implies_2(x5,x3),x1),x4)))) % U387: < d4 v21 dv12 f26 c6 t53 td9 > ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),implies_2(x2,x0)))),implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x5,x6),implies_2(x7,x8)),implies_2(x9,implies_2(implies_2(x8,x5),implies_2(x7,x5)))),x10),implies_2(x11,x10)),implies_2(implies_2(a_0(),b_0()),implies_2(implies_2(b_0(),c_0()),implies_2(a_0(),c_0())))))) % U768: < d4 v9 dv5 f8 c0 t17 td6 > is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0,x1),x2),x0),x3),implies_2(implies_2(implies_2(x4,x2),x0),x3))) % U12975: < d4 v9 dv5 f8 c0 t17 td5 > is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x1,x2)),implies_2(implies_2(implies_2(x3,x4),x1),implies_2(x1,x2)))) % --------------- Start of Proof --------------- % Derivation of unit clause U1: % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),implies_2(x2,x0))))) ....... U1 % Derivation of unit clause U4: % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),implies_2(x2,x0))))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x3)), implies_2(x4, implies_2(implies_2(x3, x0), implies_2(x2, x0)))), x5)) | is_a_theorem_1(x5) ....... R1 [B1:L0, B2:L0] % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),implies_2(x2,x0))))) ....... U1 % is_a_theorem_1(implies_2(x0, implies_2(implies_2(implies_2(implies_2(x1, x2), implies_2(x3, x2)), implies_2(x2, x4)), implies_2(x5, implies_2(x2, x4))))) ....... R2 [R1:L0, U1:L0] % Derivation of unit clause U5: % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),implies_2(x2,x0))))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x3)), implies_2(x4, implies_2(implies_2(x3, x0), implies_2(x2, x0)))), x5)) | is_a_theorem_1(x5) ....... R1 [B1:L0, B2:L0] % is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(implies_2(x1,x2),implies_2(x3,x2)),implies_2(x2,x4)),implies_2(x5,implies_2(x2,x4))))) ....... U4 % is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x1)), implies_2(x1, x3)), implies_2(x4, implies_2(x1, x3)))) ....... R2 [R1:L0, U4:L0] % Derivation of unit clause U6: % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),implies_2(x2,x0))))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x3)), implies_2(x4, implies_2(implies_2(x3, x0), implies_2(x2, x0)))), x5)) | is_a_theorem_1(x5) ....... R1 [B1:L0, B2:L0] % is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x1)),implies_2(x1,x3)),implies_2(x4,implies_2(x1,x3)))) ....... U5 % is_a_theorem_1(implies_2(x0, implies_2(x1, implies_2(implies_2(x1, x2), implies_2(x3, x2))))) ....... R2 [R1:L0, U5:L0] % Derivation of unit clause U7: % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),implies_2(x2,x0))))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x3)), implies_2(x4, implies_2(implies_2(x3, x0), implies_2(x2, x0)))), x5)) | is_a_theorem_1(x5) ....... R1 [B1:L0, B2:L0] % is_a_theorem_1(implies_2(x0,implies_2(x1,implies_2(implies_2(x1,x2),implies_2(x3,x2))))) ....... U6 % is_a_theorem_1(implies_2(x0, implies_2(implies_2(x0, x1), implies_2(x2, x1)))) ....... R2 [R1:L0, U6:L0] % Derivation of unit clause U8: % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),implies_2(x2,x0))))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x3)), implies_2(x4, implies_2(implies_2(x3, x0), implies_2(x2, x0)))), x5)) | is_a_theorem_1(x5) ....... R1 [B1:L0, B2:L0] % is_a_theorem_1(implies_2(x0,implies_2(implies_2(x0,x1),implies_2(x2,x1)))) ....... U7 % is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x3)), implies_2(x4, implies_2(implies_2(x3, x0), implies_2(x2, x0)))), x5), implies_2(x6, x5))) ....... R2 [R1:L0, U7:L0] % Derivation of unit clause U17: % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),implies_2(x2,x0))))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(implies_2(implies_2(x0, x1), implies_2(x2, x3))) | is_a_theorem_1(implies_2(x4, implies_2(implies_2(x3, x0), implies_2(x2, x0)))) ....... R1 [B1:L0, B2:L1] % is_a_theorem_1(implies_2(x0,implies_2(implies_2(x0,x1),implies_2(x2,x1)))) ....... U7 % is_a_theorem_1(implies_2(x0, implies_2(implies_2(implies_2(x1, x2), x3), implies_2(implies_2(implies_2(x3, x4), x2), x3)))) ....... R2 [R1:L0, U7:L0] % Derivation of unit clause U23: % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),implies_2(x2,x0))))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(implies_2(implies_2(x0, x1), implies_2(x2, x3))) | is_a_theorem_1(implies_2(x4, implies_2(implies_2(x3, x0), implies_2(x2, x0)))) ....... R1 [B1:L0, B2:L1] % is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(x1,x2),x3),implies_2(implies_2(implies_2(x3,x4),x2),x3)))) ....... U17 % is_a_theorem_1(implies_2(x0, implies_2(implies_2(implies_2(implies_2(implies_2(x1, x2), x3), x1), x4), implies_2(implies_2(implies_2(x5, x3), x1), x4)))) ....... R2 [R1:L0, U17:L0] % Derivation of unit clause U387: % ~is_a_theorem_1(implies_2(implies_2(a_0(),b_0()),implies_2(implies_2(b_0(),c_0()),implies_2(a_0(),c_0())))) ....... B0 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0, implies_2(implies_2(a_0(), b_0()), implies_2(implies_2(b_0(), c_0()), implies_2(a_0(), c_0()))))) ....... R1 [B0:L0, B2:L2] % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(x1) | ~is_a_theorem_1(implies_2(x1, implies_2(x0, implies_2(implies_2(a_0(), b_0()), implies_2(implies_2(b_0(), c_0()), implies_2(a_0(), c_0())))))) ....... R2 [R1:L1, B2:L2] % is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),implies_2(x2,x0)))),x5),implies_2(x6,x5))) ....... U8 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0, implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x1, x2), implies_2(x3, x4)), implies_2(x5, implies_2(implies_2(x4, x1), implies_2(x3, x1)))), x6), implies_2(x7, x6)), implies_2(implies_2(a_0(), b_0()), implies_2(implies_2(b_0(), c_0()), implies_2(a_0(), c_0())))))) ....... R3 [R2:L0, U8:L0] % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),implies_2(x2,x0))))) ....... U1 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x3)), implies_2(x4, implies_2(implies_2(x3, x0), implies_2(x2, x0)))), implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x5, x6), implies_2(x7, x8)), implies_2(x9, implies_2(implies_2(x8, x5), implies_2(x7, x5)))), x10), implies_2(x11, x10)), implies_2(implies_2(a_0(), b_0()), implies_2(implies_2(b_0(), c_0()), implies_2(a_0(), c_0())))))) ....... R4 [R3:L0, U1:L0] % Derivation of unit clause U768: % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),implies_2(x2,x0))))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x3)), implies_2(x4, implies_2(implies_2(x3, x0), implies_2(x2, x0)))), x5)) | is_a_theorem_1(x5) ....... R1 [B1:L0, B2:L0] % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x3)), implies_2(x4, implies_2(implies_2(x3, x0), implies_2(x2, x0)))), x5)) | ~is_a_theorem_1(implies_2(x5, x6)) | is_a_theorem_1(x6) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),implies_2(x2,x0))))) ....... U1 % ~is_a_theorem_1(implies_2(implies_2(x0, implies_2(implies_2(implies_2(implies_2(x1, x2), implies_2(x3, x2)), implies_2(x2, x4)), implies_2(x5, implies_2(x2, x4)))), x6)) | is_a_theorem_1(x6) ....... R3 [R2:L0, U1:L0] % is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(implies_2(implies_2(x1,x2),x3),x1),x4),implies_2(implies_2(implies_2(x5,x3),x1),x4)))) ....... U23 % is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0, x1), x2), x0), x3), implies_2(implies_2(implies_2(x4, x2), x0), x3))) ....... R4 [R3:L0, U23:L0] % Derivation of unit clause U12975: % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),implies_2(x2,x0))))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x3)), implies_2(x4, implies_2(implies_2(x3, x0), implies_2(x2, x0)))), x5)) | is_a_theorem_1(x5) ....... R1 [B1:L0, B2:L0] % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x3)), implies_2(x4, implies_2(implies_2(x3, x0), implies_2(x2, x0)))), x5)) | ~is_a_theorem_1(implies_2(x5, x6)) | is_a_theorem_1(x6) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(implies_2(implies_2(x1,x2),x3),x1),x4),implies_2(implies_2(implies_2(x5,x3),x1),x4)))) ....... U23 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x0, x1), x2), x0), x3), implies_2(implies_2(implies_2(x4, x2), x0), x3)), x5)) | is_a_theorem_1(x5) ....... R3 [R2:L0, U23:L0] % is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0,x1),x2),x0),x3),implies_2(implies_2(implies_2(x4,x2),x0),x3))) ....... U768 % is_a_theorem_1(implies_2(implies_2(implies_2(x0, x1), implies_2(x1, x2)), implies_2(implies_2(implies_2(x3, x4), x1), implies_2(x1, x2)))) ....... R4 [R3:L0, U768:L0] % Derivation of the empty clause: % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x1,x2)),implies_2(implies_2(implies_2(x3,x4),x1),implies_2(x1,x2)))) ....... U12975 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),implies_2(x2,x0)))),implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x5,x6),implies_2(x7,x8)),implies_2(x9,implies_2(implies_2(x8,x5),implies_2(x7,x5)))),x10),implies_2(x11,x10)),implies_2(implies_2(a_0(),b_0()),implies_2(implies_2(b_0(),c_0()),implies_2(a_0(),c_0())))))) ....... U387 % [] ....... R1 [U12975:L0, U387:L0] % --------------- End of Proof --------------- % PROOF FOUND! % --------------------------------------------- % | Statistics | % --------------------------------------------- % Profile 3: Performance Statistics: % ================================== % Total number of generated clauses: 100690 % resolvents: 100680 factors: 10 % Number of unit clauses generated: 100311 % % unit clauses generated to total clauses generated: 99.62 % Number of unit clauses constructed and retained at depth [x]: % ============================================================= % [0] = 2 [2] = 44 [4] = 12930 % Total = 12976 % Number of generated clauses having [x] literals: % ------------------------------------------------ % [1] = 100311 [2] = 368 [3] = 11 % Average size of a generated clause: 2.0 % Number of unit clauses per predicate list: % ========================================== % [0] is_a_theorem_1 (+)2532 (-)10444 % ------------------ % Total: (+)2532 (-)10444 % Total number of unit clauses retained: 12976 % Number of clauses skipped because of their length: 193 % N base clauses skippped in resolve-with-all-base-clauses % because of the shortest resolvents table: 0 % Number of successful unifications: 100716 % Number of unification failures: 13442 % Number of unit to unit unification failures: 26434113 % N literal unification failure due to lookup root_id table: 26 % N base clause resolution failure due to lookup table: 0 % N UC-BCL resolution dropped due to lookup table: 0 % Max entries in substitution set: 17 % N unit clauses dropped because they exceeded max values: 86415 % N unit clauses dropped because too much nesting: 6743 % N unit clauses not constrcuted because table was full: 0 % N unit clauses dropped because UCFA table was full: 0 % Max number of terms in a unit clause: 63 % Max term depth in a unit clause: 11 % Number of states in UCFA table: 143138 % Total number of terms of all unit clauses in table: 649008 % Max allowed number of states in UCFA: 528000 % Ratio n states used/total allowed states: 0.27 % Ratio n states used/total unit clauses terms: 0.22 % Number of symbols (columns) in UCFA: 39 % Profile 2: Number of calls to: % ============================== % PTUnify() = 114158 % ConstructUnitClause() = 99389 % Profile 1: Time spent in: % ========================= % ConstructUnitClause() : 0.42 secs % -------------------------------------------------------- % | | % Inferences per sec: 1549 % | | % -------------------------------------------------------- % Elapsed time: 66 secs % CPU time: 65.10 secs % %------------------------------------------------------------------------------